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| Optimal Control of a Delayed Spatiotemporal Epidemic Model |
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| KeyWord:Delayed spatiotemporal epidemic model, vaccination, hospitalization, reaction-diffusion equations, optimal control |
| Author Name | Affiliation | | Amine Alabkari | Laboratory of Analysis Modeling and Simulation, Faculty of Sciences Ben M'Sik, Hassan II University, BP 7955, Sidi Othman, Casablanca, Morocco | | Ahmed Kourrad | Laboratory of Analysis Modeling and Simulation, Faculty of Sciences Ben M'Sik, Hassan II University, BP 7955, Sidi Othman, Casablanca, Morocco | | Khalid Adnaoui | Laboratory of Analysis Modeling and Simulation, Faculty of Sciences Ben M'Sik, Hassan II University, BP 7955, Sidi Othman, Casablanca, Morocco | | Hassan Laarabi | Laboratory of Analysis Modeling and Simulation, Faculty of Sciences Ben M'Sik, Hassan II University, BP 7955, Sidi Othman, Casablanca, Morocco |
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| Abstract: |
| This study presents an advanced delayed spatiotemporal epidemiological model that incorporates a Holling type II incidence rate to capture the saturation effects observed in disease transmission dynamics during the COVID-19 pandemic. The model integrates two crucial intervention measures - vaccination of susceptible individuals and hospitalization of severe cases - while accounting for both spatial diffusion and the latent period within the epidemic compartments. This framework facilitates the precise optimization of vaccination and hospitalization strategies as functions of spatial location and temporal evolution, yielding new insights into spatially targeted public health interventions. We rigorously analyze the model equilibrium points, establishing conditions for their existence and local stability. An optimal control problem is formulated, uniquely considering the combined effects of spatial diffusion and latent period, with controls dynamically varying across space and time. The well-posedness of the control problem is verified, supported by proofs of existence, uniqueness, positivity, and boundedness of the strong solution. First-order necessary optimality conditions are derived, characterizing the optimal vaccination and hospitalization strategies through state and adjoint variables. Numerical simulations across diverse intervention scenarios demonstrate the effectiveness of adaptive, space-time-specific control strategies in mitigating COVID-19 transmission. This work offers a novel mathematical and computational approach to the optimal spatiotemporal management of epidemic control measures. |
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